Rotating shafts have a vast application in various industries especially in the aerospace industry such as engines, compressors and turbines. The researchers have performed considerable efforts on the rotating shafts’ dynamic behavior because of their sensitivity to the rotor specifications and different parameters such as supports. In this paper by employing a pipe elbow element, an especial finite element formulation is derived to investigate dynamic behavior of rotating shaft in the presence of support clearance. The proposed element consists of four nodes with twenty-four degrees of freedom, which also accounts for the shear and gyroscopic effects. Within a finite element analysis framework, the focus of the paper is proposing a formulation to account for the dynamic behavior of a rotating shaft with much less number of elements. The element is implemented in a finite element code and then is used to model and analyze some rotating shaft examples. In order to verify the developed formulation, results are compared with those obtained from other schemes reported in the literature.